Top Cross Section Measurement

Top Quarks in Year 1
Akira Shibata
New York University
ATLAS Workshop of the Americas @ NYU
5 Aug, 2009

Can Top change our perspective?
• Why is top so heavy (10 water molecules)? Any
special role in EW symmetry breaking?
• Does it play even more fundamental role than
Higgs mechanism + Yukawa coupling?
• If there is new physics signal lighter than top,
does the top quark decay into them?
• Could non-SM physics ﬁrst manifest itself in non-
standard couplings of the top quark?
• Top quark can be measured at signiﬁcant
precision at the LHC to answer these questions.
• Top quark has been an extremely productive
ground for speculation and searches at Tevatron.

Workshop of the Americas ’09 2 akira.shibata@nyu.edu

New Physics via Top Decay
• The ﬁnal state of a t¯system is primarily clas-
t
siﬁed by the decay modes of the two W bosons:

• Various decay modes make top
physics interesting and useful
• The top interfere with a number of
new physics signatures.
• Typical search modes:
• Lepton + jets (e/mu)
• Dileptonic
• All hadronic
• Tau channels
• E.g. If mW<mH+<mt and tanβ>>1, top
can decay into charged higgs,
enhancing the τ lepton rate.


New Physics via Top Decay
• The ﬁnal state of a t¯system is primarily clas-
t
siﬁed by the decay modes of the two W bosons:

• Various decay modes make top
physics interesting and useful
Name
Fully Hadronic
Signature
jets
BR
45.7%
xsec at 10 TeV
191.5 pb • The top interfere with a number of
new physics signatures.
•
Lepton + Jets e + jets 17.2% 71.9 pb
µ + jets 17.2% 71.9 pb Typical search modes:
Dilepton eµ + jets
µµ + jets
3.18%
1.59%
13.3 pb
6.67 pb • Lepton + jets (e/mu)
ee + jets 1.59% 6.67 pb
• Dileptonic
Tau + Jets
Lepton + Tau
τ + jets
τ + e/µ + jets
9.49%
3.54%
39.8 pb
14.8 pb • All hadronic
Tau + Tau τ + τ + jets 0.49% 2.06 pb
• Tau channels
total all 100% 419 pb
• E.g. If mW<mH+<mt and tanβ>>1, top
can decay into charged higgs,
• Diboson (ME: MC@NLO, PS: Herwig + Jimmy) enhancing the τ lepton rate.
The MC samples were generated with 5 TeV against 5 TeV beam energy. CTEQ 6 PDF set
was used and the top mass was set to be 172.5 GeV. Alpgen MLM matching threshold was set to akira.shibata@nyu.edu
Workshop of the Americas ’09 3

80 90 100 110 120 130 140 150 160
MH+ [GeV]

Search for Charged Higgs
FIG. 10: Observed (blue) and expected (red) limit with one standard deviation band (yellow) on Br(t → H + b)
of charged Higgs mass for simultaneous ﬁt of Br(t → H + b) and σtt in the tauonic model.
¯

DØ Run II Preliminary

MH+ [GeV]
+
H # cs H+ # " ! DØ Note 5715-CONF
180 Expected limit 95% CL
Expected limit 95% CL

Excluded 95% CL Excluded 95% CL
160

140 tauonic
leptophobic
120

100

80
1 10
tan $

FIG. 11: Observed (blue) and expected (red) limit with one standard deviation band (yellow) on charged Hi
function of tan β.

Research Council and WestGrid Project (Canada), BMBF (Germany), A.P. Sloan Foundation, Civil
and Development Foundation, Research Corporation, Texas akira.shibata@nyu.edu
Advanced Research Program, and the A

80 90 100 110 120 130 140 150 160
MH+ [GeV]

Search for Charged HiggsFIG. 10: Observed (blue) and expected (red) limit with one standard deviation band (yellow) on Br(t → H + b)
of charged Higgs mass for simultaneous ﬁt of Br(t → H + b) and σtt in the tauonic model.
¯

DØ Run II Preliminary

MH+ [GeV]
+
H # cs H+ # " ! DØ Note 5715-CONF
180 Expected limit 95% CL
Expected limit 95% CL

Excluded 95% CL Excluded 95% CL
160

140 tauonic
leptophobic
120

100

80
1 10
tan $

Good tau/jet calibration and backgroundand expected (red) limit with one standard deviation band (yellow) on charged Hi
FIG. 11: Observed (blue) control is essential for this search.

Not a “Day-1 physics”
function of tan β.

Research Council and WestGrid Project (Canada), BMBF (Germany), A.P. Sloan Foundation, Civil
and Development Foundation, Research Corporation, Texas akira.shibata@nyu.edu
Advanced Research Program, and the A

onance Search New Physics into Top overlapping
ν e
¯

Fraction/25GeV
0.22
ulate pp invariant → t for tt pairs
the → X mass t
(a) SM tt
0.2
pp → X → t t
for a bump!
¯ b W + 0.18
X!tt MX=450GeV
X!tt MX=650GeV

pp → b ¯ → W − t W + t ¯
0.16
b
the dominant background is Standard
0.14 X!tt MX=1000GeV

pp → b ¯ → W − t W + t ¯ 0.12
el tt! b t boosted 0.1
DØ Preliminary

pp → g g → gt g t ¯
challenges for large masses (> 1 TeV)
0.08
0.06

ghly boosted g → gt ¯
pp → topgquarks g t X 0.04
0.02
00 200 400 600 800 1000 1200
verlapping decay products Mtt [GeV]
construct “top quark jets” ¯
t boosted Topcolor Z’ excluded < 800 GeV.
If new physics is leptophobic, Kaluza-Klein gluon excluded < 1TeV
FIG. 1: Shape comparison of expected tt invariant mass distribut
s limits depend on the theoretical model
they may couple strongly to
(histogram) compared to resonant production from narrow-wid
for (a) 3 jet events and (b) ≥ 4 jet events.
ematic errors similar to those for tt W−
s-section Otherwise, dimuon is a
top.
¯
clearer signature.
q b VI. SYSTEMATIC
¯
q
The systematic uncertainties can be classified as those a
of any of the signal or background invariant mass distri
overlapping 8
normalization include the theoretical uncertainty on the S
luminosity (6.1%) [29] and the uncertainty of lepton identifi
The systematic uncertainties affecting the shape of the inv

onance Search New Physics into Top overlapping
ν e
¯

Fraction/25GeV
0.22
ulate pp invariant → t for tt pairs
the → X mass t
(a) SM tt
0.2
pp → X → t t
for a bump!
¯ b W + 0.18
X!tt MX=450GeV
X!tt MX=650GeV

pp → b ¯ → W − t W + t ¯
0.16
b
the dominant background is Standard
0.14 X!tt MX=1000GeV

pp → b ¯ → W − t W + t ¯ 0.12
el tt! b t boosted 0.1
DØ Preliminary

pp → g g → gt g t ¯
challenges for large masses (> 1 TeV)
0.08
0.06

ghly boosted g → gt ¯
pp → topgquarks g t X 0.04
0.02
00 200 400 600 800 1000 1200
verlapping decay products Mtt [GeV]
construct “top quark jets” ¯
t boosted Topcolor Z’ excluded < 800 GeV.
If new physics is leptophobic, Kaluza-Klein gluon excluded < 1TeV
FIG. 1: Shape comparison of expected tt invariant mass distribut
s limits depend on the theoretical model
they may couple strongly to
(histogram) compared to resonant production from narrow-wid
for (a) 3 jet events and (b) ≥ 4 jet events.
ematic errors similar to those for tt W−
s-section Otherwise, dimuon is a
top. Good control of SM top and jet
q ¯
b
clearer signature. ¯
q resolution & jet substructure.
VI. SYSTEMATIC

The systematic“Day-1 physics”those a
Not a uncertainties can be classified as
of any of the signal or background invariant mass distri
overlapping 8
normalization include the theoretical uncertainty on the S
luminosity (6.1%) [29] and the uncertainty of lepton identifi
The systematic uncertainties affecting the shape of the inv

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State of the Art at
Tevatron
Cross-Section Measurement
• Semileptonic channel
• High branching ratio (~36/81)
• Event over-constrained
• Manageable background
• Dileptonic channel
• Low background
• Low branching ratio (~9/81)
• Event under-constrained
• Fully hadronic channel
• Event fully constrained
• Huge QCD and comb. background
• Lepton + Track
• Highly inclusive
• Different systematics for track
performance.
8% precision all combined (summer 2008)

Graph

!t t [pb] RULES OF THUMB
1.2

1000 CDF Results ! Running at 10 TeV takes ~twice as 1
much data as 14 TeV for equivalent

Xsec relative to 14 TeV
LHC 14 TeV @ 100pb-1 Expectations (CSC) 0.8
sensitivity W, Z
Theoretical NLO (pp)
0.6 Top
800 Theoretical NLO (pp) ! Running at 8 TeV takes ~twice as Z' (2 TeV)
Theoretical NLO+NNLL much data as 10 TeV for equivalent ee/μμ/eμ 0.4

sensitivity
NLO+NNLL Scale Uncertainty 0.2
600
0
e/μ+jets
Graph

12 ! Below 8 TeV things go “pear 0 2 4 6 8 10 12 14 16
! [pb]

Produced by Akira Shibata and Ulrich Husemann
tt

10 shaped” quickly. CM Energy (TeV)
8
400 6
4
2
Produced by Akira Shibata and Ulrich Husemann

We know a lot about top 4

200 1 1.5 2 2.5 already, from Tevatron and
[hep-ph/0204244]
[arXiv:0907.2527]
theorists, but LHC will show
0
us a LOT more. Priced
0 2 4 14 6 8 10 12 steeply in TeV, much more
s [TeV] so than the background.
NB: Large uncertainty in theory due to PDF not shown.
CSC assumed 5% luminosity

Dhiman Chakraborty The Top Quark

First year detector is less than ideal Top Physics Potential
Numerous uncertainties that Triggering

affect measurements with the W tb coupling, |Vtb |
Lepton ID
+
early data: Top mass, width, spin, charge
Top mass constraint
• Trigger efﬁciency W mass constraint
• Non-uniform detector Initial state rad.
• Lepton identiﬁcation Luminosity W+
ν
• Missing Et calibration and tails Production
PDF section
cross
e + /¯
q
Missing Et
• Light/b jet energy scale t
• QCD activity (MI, ISR/FSR) Resonant
production ?
Pile-up X
b
• Beam related issues (Pile-up, Underlying event
Production Yukawa coupling ?
Luminosity) kinematics B-tagging
!
• PDF Spin e−/q ¯
t Bjet energy scale
• Background normalization polarization
Kinematic fit B fragmentation
• other unknown unknowns Anomalous couplings ?

?
Jet reconstruction
Real performance need to be estimated from real data. Top is sensitiveRare/non-SM decays ?
Light jet e scale
to a variety of effect but it will also provide means for calibrationBranching fractions ? state rad.
Final
based on constraints in masses and decays.
Workshop of the Americas ’09 9 Oct 2006
9 8
akira.shibata@nyu.edu

• We will look into a very recent
study on single and di-lepton cross
section measurements.
• Much learned about the full approval
process: INT approved, PUB approval
in progress.
• Used the “MC08” Monte Carlo
samples with full Geant 4 simulation
(rel 14.2.20.x) Timeline (Dilepton note)
Apr 28. need for a summer note announced
• Collision energy is 10 TeV. Plots and May 06. editors appointed
tables are normalized to 200 pb-1. May 12. discuss selection
May 22. object and event selection agreed
May 26. discuss systematics
May 29. systematics treatment agreed
June 02. note submitted and comments received
June 05. top group approval
July 13. INT approval
July 28. Sent to collaboration review
cf: https://twiki.cern.ch/twiki/pub/Atlas/OperationModelOverviewDocument/physics_policy.pdf

Strategy with the First Data
Do the simplest thing we can do: “cut and count”

N = L σtT BR ϵtrigϵlep A + B
pray for a large number
but expect large uncertainty. part data driven,
May not be available quickly to be estimated part MC driven
well known in SM from data
sensitive to
theoretical
uncertainty
Realistically, e and mu single lepton and dilepton channels
only. Taus, too difﬁcult to calibrate. Fully hadronic too
difﬁcult to trigger.


Object Selection
• Trigger Not fully optimized (ongoing study in Top
• EF_e15_medium OR EF_mu15 Reconstruction Group) but emphasis on
• Electrons simplicity and robustness, relying only on
the clearest feature of the events and
• egamma isEM ElectronMedium objects.
• pT > 20GeV
• |η| <1.37 or 1.52<|η| <2.47 • Jets
• etcone20 < 6GeV • Cone4TowerJets, with pT>
• Muons 20GeV, |η| < 2.5.
• STACOmuons: isCombined. • Overlap removal: no selected
• pT > 20GeV electrons within ∆R = 0.2
• |η| < 2.5 • No b-tagging
• etcone20 < 6GeV • MEt
• No overlap with jets within ∆R = 0.3 • MEt_RefFinal


24 all jets 22 435jets
all

Event Selection - Single Lepton
1
24 all jets match 0 20 40 60 80
235 100 120 1
Missing tran

24.1.1 Jet N 0 10i 20GeV

Figure 8: Missing transverse ener

•
Jet Multiplicity (Pt > 20 GeV)

One good lepton jet multiplicity distribution (right)

Events

entry (11 bins)
entry (11 bins)
140

•
4
based10 background estimations afte

entry (11 bins)
400
MET > 20 GeV (reduces QCD and Z) 1000 ATLAS Preliminary
ATLAS Preliminary

•
120 Simulation 350
Simulation 103

3 Jets with Pt > 40 GeV DRAFT
July 27, 2009 – 22 : 56 (reduces W)

Events
Events

Events
Events

Events
400
July 27, 2009 – 22 : 56 DRAFT 14 15 103

•
104
800 tt dilepton, ee
100 e+jets t t dilepton,tt dilepton, ee
eµ 104 300
4 Jets with Pt > 20 GeV (further reduces W)
120
tt other t t other
single top 102 350

•
single top tt other 250
100 Z+jets 300

ReconstructTable 3: from of events which pass the various muon tt¯ signal criteria for ¯
top Number 3 highest pt jet comb
3
10
3
600 Z+jets80 W+jets single top10
102 10 250

•
W+jets WW/WZ/ZZ
80 Z+jets 200
Table 2: Number of events which pass the various electron selection criteria for the selection and for the the t t signal and for the
mostRequire thereatis one dijet comb−1 (left columns) and 14 TeV normalised to 14 TeV normalised to
relevant backgrounds, 10 TeV normalised to 200 pb with |Mw-Mdijet| columns) and
WW/WZ/ZZ ATLAS Preliminary
102 60 24 all jets Simulation W+jets 10
2 200 22 435jets
all
most relevant backgrounds, at 10 TeV normalised to 200 pb−1 (left 400
ATLAS Preliminary 60
1 150 A

100 pb−1 (right columns). The statistical errors due to limited Monte Carlotop) areMonte Carlo Statistics 40 also shown.
<10 GeV (further(right columns).W and singledue to limited also shown.
100 pb−1 reduces The statistical errors Statistics
Simulation 150 S
WW/WZ/ZZ 0 20 40 60 80 100 120
are 10 40
24 all jets match 235

•
10 10 Missing
100 100
Signal efﬁciency ~10% analysis
200 ATLAS Preliminary
20 Simulation 50
Electron Muon analysis 20 24.1.1 Jet N 0 10i 20GeV
50
ejets μjets
1 1
120 140 160 180 200Figure 8: 0
−1140 160 −1 200 14TeV00 −1 ) 3 0 1020 Missing transverse en
10TeV (200 ) 20 pb−1 40 10TeV (200 pb (100 pb 180
100 120 )
60 80 14TeV ) 1
20 (100 60 280 100 4
0 1 pb
0 40 60 80 100 120 1 Jet Multiplicity (Pt > 20 GeV)

0 0 40 5 6 7 8 9 1 2 3 4 5
0 2 Missing transverse energyNumber of Jets 10
4 6 8 0 Missing tran
+mt cut default cut W +mt cut tdefault +MW cut 140 t0cut Jet Multiplicity (Pt jet20 GeV) 8 multiplicity distribution (righ

Missing transverse energy [GeV] 0 [GeV]
Sample default Sample cut
+MW default +MW +M cut +m cut +m

entry (11 bins)
0 2

entry (11 bins)
2 4 6 > 10
1400
ATLAS based background estimations a

entry (11 bins)
400 Jet M
ttbar 2600 ± 15 ttbar ± 11 3144 ± 7
1286 581 17 1584 ± 12 1262 ± 8 561
2555 712 3274 1606 755 Jet Multiplicity (Pt >Preliminary 20 GeV)
ATLAS Preliminary Missing transverse energ
Figure 9:
W+jets 1305 ± 33 W+jets± 20 8: Missing transverse energy distribution (left)1200Multiplicity two opposite distribution (left) afterFig. 181: Jet 350
448 Figure 1766 ± 9
108 44 628 ± 27 148 ± 13 Figure 10:after 319 transverse energy signed leptons be found in Multiplicity oppo
761 241 60 199: Jet Missing 120 (Pt > 20 GeV)Simulation and requiring two (Pt
1052 requiring 98 Simulation
multiplicity distribution (right)eaft
Fig. (can

210 ± 9 single top multiplicity± 9
jet 227 distribution ± 6 after ± 4cuts 23 3
183 (right) 33 all jet(except the Ndistribution 25 jets/Jet Ntt0dilepton, eµbased background estimations afte
multiplicity jets > 1 cut) for jets ee dilepton signal stack.eps) found
Multiplicity match/Jet N 20 10iGeV)
(Pt 0 20GeV(can andbeMC jets ../../../eps/default/emu/all
../../../eps/default/ejets/all(right) after all cuts (except the N in > 1 cut) for µ je
Fig. 199: Jet

Events
Events

Events
>

Events

Events
single top 81 ± 6 27 ± 3 98 67 227
10 99 ../../../eps/default/ee/all 10i 20GeV stack.eps) 400

148 ± 4 Z→ ll +jets background estimations2after all cuts. The 8 84 120 normalized to 200pb tsingle topThe samples 350 normalized to 200p
based samples are 23 100 3 −1 . 300
13 ± 1 based background estimations after all tcuts. are
104 tt dilepton, ee 1000 mu+jets 104
tt dilepton, ee
Z→ ll +jets 43 ± 2 11 ±± 4
144 1 115 ±
49 35
tt other other

¯ single top tt other
hadronic t t 10 t ¯3
16 ± 3 hadronic±t2 2 ±± 2
11 1 11 ± 1
5 4
2±1 0.0 35 100 17
800 7 Z+jets 300 250
The scale factors are deﬁned as !
3
¯ 10 Z+jets 80 W+jets single top10
¯
Events

W+jets 1 µµ 3 64 Expected number of selected events for the ee channel selection for 20
Table2 1: 200

Events
W bb 21 ± 1 W bb 7 ± 1 4 2 ±± 2
32 0 44 ± 1
10 15 ±
3 10 19 4 WW/WZ/ZZ 250
10 tt dilepton,
WW/WZ/ZZ only 26
80
180 measured in data from200
Z+jets
tt dilepton, µµ
1 shown for the9last 60 columnsATLAS Preliminary but2 they are fully taken into ac Z events, an
W cc ¯ W cc¯ 19 tt 6
600 two 3 for readability, 10 200
7 ± 1 ATLAS2Preliminary the S/B calculation. The column labeledt ”true” represents the effect of geome
t other convolution of kinematic,
a
2 other Simulation W+jets
10 160
60
WW 11 ± 2 WW 6 ± 1 3 2 ±± 2
14 1 7 4 ± 1 and 7 140
single top
0.4 3 0.7 150 applyi
10 Simulation
Z+jets 400 WW/WZ/ZZ Dilepton branching ratios inclu
150
WZ 3 ± 1 WZ 1 ± 1 ±0
05 ± 1 4 ± 1 0.2W+jets The 107 120labeled ”fake”0.8
2 1
± 0.2 0.4 column 40 3 40 shows the number oftop 10 which failed the truth-ma
single
events 100
ATLAS Preliminarydecay. From MC@NLO
top pair
10 100
Z+jets
ZZ 0.4 ± 0.1 ZZ0.2 ± 0.1 2 0.1 ±± 0.1
0.5 0.1 0.2 ± 0.1 0.1WW/WZ/ZZ 0.1
0.5 0.2 0.0
± 0.7 100 0.3
200 0.1
10
ATLAS Preliminary
20
lepton sel. inv. mass cut ET 1 0.05)% and BR(t t → eµ )
20 Simulation
W+jets (1.64 miss cut jet cut trigger
± 50 ¯
Signal 2600 Signal 1286 581
3144 2555 1262712 561 1
1584 Simulation 3274 80
1606 755 50
322 7 A(ee) = (16.5 ± 220 A(µ µ ) = (
0.4)%, 214±6 120
1
0 20 40 60 80 100 120 140 160 180 200 ¯ dilepton
0 t t 600 400 1 60 280 351 4 4 140 160 180 200 9261
20 0
0
3100 120 5 6 6 WW/WZ/ZZ 0 10 00 40 1 60 2 80 3100 4
8 1020
Background 1715 Background598 154 1144 799transverse energy [GeV]
374201 96 2 143 8
0 15 Jet Multiplicity Preliminary10 on MC 9
13 (Pt > Based10 simulation for si
10 2199 1497 40 495 0 Missing
Missing
¯
t t other3.2 Missing transverse energyNumber of Jets
0 ATLAS 6
[GeV]
20 GeV) 8±1 2
0
S/B 1.5 S/B 2.1 3.8
1.4 2.2 2.0 3.4 3.5 5.82.2 20 5.3 2 4 8
for an integrated luminosity of 200
single top 27 Jet Multiplicity (Ptmiss2018
akira.shibata@nyu.edu 9
25 9±2 Je
Simulation
Workshop of the Americas ’09 13 > GeV)
8 T 9 and jet multiplicity distributi
1
0 20 40 60 80 100 120 140 160 180 200
0
0 1 2 3 4 5 6 7 EFigure10 Missing transverse en
9: +2

ment, in percent, for electrons and muons. The entries in bold indicate the errors which are finally quoted
and constitute the total estimates. The final summed totals do not include the luminosity error which is
quoted separately.

Source
Cut and Count method
e-analysis µ -analysis
• Lepton efficiency to be estimated using
Fit method
tag and probe
e-analysis µ -analysis

•
default +MW cut default +MW cut +MW cut +MW cut
(%) (%) (%) (%) (%) Applicable after correction in η, pT
(%)
Stat. ± 2.5 ± 3.4 ±2.3 ±3.1 ± 14.1 and isolation.
± 15.2

•
Lepton ID eff. ±1.0 ±1.0 ±1.0 ±1.0 ± 1.0 ± 1.0
Lepton trig. eff. ±1.0 ±1.0 ±1.0 ±1.0 ± 1.0 W+Jets is the dominant background
± 1.0
50% W+jets
20% W+jets
JES (10%,-10%)
±25.1
±10.0
±17.4
±7.0
±28.1
±11.2
±19.8
±7.9
+24.8-23.4 +15.9-19.1 +20.5-22.3 +11.9-17.9
± 3.3
± 1.5
-14.4
• Studied data-driven estimation based
± 5.6
± 2.6
on Z/W ratio. Estimates 20% unc.
-15.4
JES (5%,-5%)
PDFs
ISR/FSR
+12.3-11.9 +8.6-9.3
±1.6
+9.1-9.1
± 1.9
+7.6-8.2
+10.4-10.9
±1.2
+8.2-8.2
+6.1-8.4
± 1.4
+5.2-8.3
•
-3.7
± 1.9
-12.9
-3.9
The analysis rather sensitive to JES
± 1.4
variation.
-12.9
Signal MC
Back. Uncertainty
Fitting Model
±3.3
±0.6
-
±4.4
±0.4
-
±0.3
±0.5
-
±2.8
±0.4
-
± 4.5
-
± 3.3
• ± 1.4
Constant scaling of jet energy applied
-
(MEt varied correspondingly).
± 4.7

•
10% Lumi. ±11.6 ±11.2 ±11.4 ±11.1 ±10 ±10
20% Lumi. ±23.2 ±22.3 ±22.8 ±22.2 ±20 ISR/FSR effects evaluated using Pythia
± 20
Tot. without Lumi. +18.8-18.5 +14.4-15.2 +17.5-17.7 +11.9-14.7
• Variation of ΛQCD and cutoff leads to
+6.4 -14.9 +6.0 - 14.7

large variation.
Bold is used in final combination
538 6.7 Cross-section Evaluation with the Baseline analysis
With the first 200 pb−1 ¯
of data, we demonstrate that we can observe a t t
• By far the dominant effect is the
signal anduncertainty on Luminosity.
determine its
540 production cross-section. In the default scenario with 5% JES uncertainty and 20% uncertainty on the
¯
W+jets background this simple method yields the following uncertainty on the t t cross-section using the
542 default lepton analysis plus the MW cut in the Cut and Count method:

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